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<H1><A NAME="SECTION02100000000000000000"></A>
<BR>
Preface to the Third Edition
</H1>

<P>
Since the release of version 2.0 of the LAPACK software and the second edition
of the Users' Guide in 1994, LAPACK has been expanded further and has become an
even wider community effort.
The publication of this third edition of the
Users' Guide coincides with the release of version 3.0
of the LAPACK software.  Some of the software contributors to this release
were not original LAPACK authors, and thus their names have been
credited in the routines to which they contributed.

<P>
Release 3.0 of LAPACK introduces new routines, as well as extending
the functionality of existing routines.  The most significant
new routines and functions are:
<DL COMPACT>
<DT>1.
<DD>a faster singular value decomposition (SVD),
computed by divide-and-conquer (xGESDD)
 <DT>2.
<DD>faster routines for solving rank-deficient least squares problems:

<UL><LI>using QR with column pivoting (xGELSY, based on xGEQP3)

<LI>using the SVD based on divide-and-conquer (xGELSD)
    
</UL>
 <DT>3.
<DD>new routines for the generalized symmetric eigenproblem:

<UL><LI>xHEGVD/xSYGVD, xHPGVD/xSPGVD, xHBGVD/xSBGVD: faster routines
         based on divide-and-conquer

<LI>xHEGVX/xSYGVX, xHPGVX/xSPGVX, xHBGVX/xSBGVX: routines based on
         bisection/inverse iteration to more efficiently compute
         a subset of the spectrum
      
</UL>
<DT>4.
<DD>faster routines for the symmetric eigenproblem using the
     ``relative robust representation'' algorithm
     (xSYEVR/xHEEVR, xSTEVR, xSTEGR)
 <DT>5.
<DD>faster routine for the symmetric eigenproblem using ``relatively robust
    eigenvector algorithm'' (xSTEGR, xSYEVR/xHEEVR, SSTEVR)
 <DT>6.
<DD>new simple and expert drivers for the generalized nonsymmetric
    eigenproblem (xGGES, xGGEV, xGGESX, xGGEVX), including error bounds
 <DT>7.
<DD>a solver for the generalized Sylvester equation (xTGSYL), used in 5)
 <DT>8.
<DD>computational routines (xTGEXC, xTGSEN, xTGSNA) used in 5))
 <DT>9.
<DD>a blocked version of xTZRQF (xTZRZF), and associated xORMRZ/xUNMRZ
</DL>

<P>
All LAPACK routines reflect the current version number with the
date on the routine indicating when it was last modified.
For more information on revisions to the LAPACK software or this Users'
Guide please refer to the LAPACK <TT>release_notes</TT> file on netlib.
Instructions for obtaining this file can be found in
Chapter&nbsp;<A HREF="node6.html#chapessentials">1</A>.

<P>
The following additions/modifications have been made to this third edition
of the Users' Guide:

<P>
Chapter&nbsp;<A HREF="node6.html#chapessentials">1</A> (Essentials) 
includes updated information on accessing LAPACK and related projects 
via the World Wide Web.

<P>
Chapter&nbsp;<A HREF="node19.html#chapcontents">2</A> (Contents of LAPACK) has been expanded to discuss
the new routines.

<P>
Chapter&nbsp;<A HREF="node60.html#chapperformance">3</A> (Performance of LAPACK) has been updated
with performance results for version 3.0 of LAPACK.

<P>
Chapter&nbsp;<A HREF="node72.html#chapaccstab">4</A> (Accuracy and Stability) has been extended
to include error bounds for generalized least squares.

<P>
Appendices&nbsp;<A HREF="node141.html#chapcomp">A</A> and&nbsp;<A HREF="node143.html#chapauxil">B</A> have
been expanded to cover the new routines.

<P>
Appendix&nbsp;<A HREF="node148.html#chapqreflawn">E</A> (LAPACK Working Notes) lists a number of new
Working Notes, written during the LAPACK&nbsp;2 and ScaLAPACK 
projects (see below) and published by the University of Tennessee.
The Bibliography has been updated to give
the most recent published references.

<P>
The Specifications of Routines have been extended and updated to cover
the new routines and revisions to existing routines.

<P>
The original LAPACK project was funded by the NSF. Since its completion,
four follow-up projects, LAPACK&nbsp;2, ScaLAPACK, ScaLAPACK&nbsp;2 and LAPACK&nbsp;3 have
been funded in the U.S. by the NSF and ARPA in 1990-1994, 1991-1995,
1995-1998, and 1998-2001, respectively.  

<P>
In addition to making possible
the additions and extensions in this release, these grants have 
supported the following closely related activities.

<P>
A major effort is underway
to implement LAPACK-type algorithms for distributed memory
<A NAME="506"></A> machines.
As a result of these efforts,
several new software items are now available on netlib.  The new
items that have been introduced are distributed memory versions of the
core routines from LAPACK; sparse Gaussian elimination - SuperLU, SuperLU_MT,
and distributed-memory SuperLU; a fully parallel package to solve a symmetric
positive definite sparse linear system on a message passing
multiprocessor using Cholesky factorization<A NAME="507"></A>; a package based on
Arnoldi's method for solving large-scale nonsymmetric, symmetric, and
generalized algebraic eigenvalue problems<A NAME="508"></A>; 
and templates for sparse
iterative methods for solving <I>Ax</I>=<I>b</I><A NAME="509"></A>.
For more information on the
availability of each of these packages, consult the following URLs:
<BLOCKQUOTE>
<TT>http://www.netlib.org/scalapack/</TT> 
<BR>
<TT>http://www.netlib.org/linalg/</TT>

</BLOCKQUOTE>

<P>
Alternative language interfaces to LAPACK (or translations/conversions
of LAPACK) are available in Fortran&nbsp;95, C, and Java. 
For more information consult Section &nbsp;<A HREF="node18.html#relsoftware">1.12</A> or the following URLs:
<BLOCKQUOTE>
<TT>http://www.netlib.org/lapack90/</TT> 
<BR>
<TT>http://www.netlib.org/clapack/</TT> 
<BR>
<TT>http://www.netlib.org/java/f2j/</TT>

</BLOCKQUOTE>

<P>
The performance results presented in this book were obtained using
computer resources at various sites:

<UL><LI>Compaq AlphaServer DS-20, donated by Compaq Corporation, and
located at the Innovative Computing Laboratory, in
the Department of Computer Science, University of Tennessee, Knoxville.

<P>

<LI>IBM Power&nbsp;3, donated by IBM, and located at the Innovative Computing
Laboratory, in the Department of Computer Science, University of
Tennessee, Knoxville.

<P>

<LI>Intel Pentium III, donated by Intel Corporation, and
located at the Innovative Computing Laboratory, in
the Department of Computer Science, University of Tennessee, Knoxville.

<P>

<LI>Clusters of Pentium IIs, PowerPCs, and Alpha EV56s, located at the LIP
(Laboratoire de l'Informatique du Parall&#233;lisme), ENS (&#201;cole
Normale Sup&#233;rieure), Lyon, France.

<P>

<LI>SGI Origin 2000, located at the Army Research Laboratory
in Aberdeen Proving Ground, Maryland, and supported by the DoD High
Performance Computing Modernization Program ARL Major Shared Resource Center
through Programming Environment and Training (PET) under Contract Number
DAHC-94-96-C-0010, Raytheon E-Systems, subcontract no. AA23.

<P>

</UL>

<P>
We would like to thank the following people, who were either not
acknowledged in previous editions, or who have made significant
additional contributions to this edition:
 
Henri Casanova,
Tzu-Yi Chen,
David Day,
Inderjit Dhillon,
Mark Fahey,
Patrick Geoffray,
Ming Gu,
Greg Henry,
Nick Higham,
Bo K&#229;gstr&#246;m,
Linda Kaufman,
John Lewis,
Ren-Cang Li,
Osni Marques,
Rolf Neubert,
Beresford Parlett,
Antoine Petitet,
Peter Poromaa,
Gregorio Quintana,
Huan Ren,
Jeff Rutter,
Keith Seymour,
Vasile Sima,
Ken Stanley,
Xiaobai Sun,
Fran&#231;oise Tisseur,
Zachary Walker, and
Clint Whaley. 
<BR>

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<ADDRESS>
<I>Susan Blackford</I>
<BR><I>1999-10-01</I>
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